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Duan, Wu and Zhou (FOCS 2023) recently obtained the improved upper bound onthe exponent of square matrix multiplication $\omega<2.3719$ by introducing anew approach to quantify and compensate the ``combination loss" in prioranalyses of powers of the Coppersmith-Winograd tensor. In this paper we showhow to use this new approach to improve the exponent of rectangular matrixmultiplication as well. Our main technical contribution is showing how tocombine this analysis of the combination loss and the analysis of the fourthpower of the Coppersmith-Winograd tensor in the context of rectangular matrixmultiplication developed by Le Gall and Urrutia (SODA 2018).

Faster Rectangular Matrix Multiplication by Combination Loss Analysis